Limitations in the understanding
of mathematical logic
by novice computer science students

Abstract of Doctoral Thesis

Vicki L. Almstrum

The University of Texas at Austin, 1994
Supervisors: Ralph W. Cain and Nell B. Dale

This research explored the understanding that novice computer science
students have of mathematical logic. Because concepts of logic are at the
heart of many areas of computer science, it was hypothesized that a solid
understanding of logic would help students grasp basic computer science
concepts more quickly and would better prepare them for advanced topics
such as formal verification of program correctness. This exploratory study
lays the groundwork for further investigation of this hypothesis.

Data for the study were the publicly available versions of the Advanced
Placement Examination in Computer Science (APCS examination) and files containing
anonymous individual responses of students who took these examinations.
A content analysis procedure was developed to provide reliable and valid
classification of multiple-choice items from the APCS examinations based
on the relationship between concepts covered in each item and the concepts
of logic. The concepts in the computer science subdomain of logic were clarified
by means of a taxonomy developed for use in this study.

Thirty-eight experts in computer science education were judges in the
content analysis of the multiple-choice items. The judges' ratings provided
criteria for grouping items into strongly related and not strongly related
partitions. In general, the mean proportion of student respondents that
correctly answered the items in a partition was lower for the strongly related
than for the not strongly related partition, with a smaller standard deviation.
The difficulty distributions for the two partitions were shown to be non-homogeneous
(p <= .002), with the difficulty distribution for the strongly related
partition skewed more towards the "very difficult" end of the
distribution.

The results of this study suggest that novice computer science students
experience more difficulty with concepts involving mathematical logic than
they do, in general, with other concepts in computer science. This indicates
a need to improve the way in which novice computer science students learn
the concepts of logic. In particular, pre-college preparation in mathematical
logic and the content of discrete mathematics courses taken by computer
science students need to be scrutinized.

Copyright (c) 1994 by Vicki Lynn Almstrum, Ph.D. Presentation
of this material by the Department of Computer Sciences at the University
of Texas at Austin was made possible under a limited license grant from
the author, who has retained all copyrights in the works.